CPhill

I believe there is a formula for this that  is similar to Heron's 

s =  (  15 + 36 + 39) /  2  =    90/ 2  = 45

Area =  (4/3)  sqrt   [ s ( s - m1) (s - m2) (s - m3) ] = 

(4/3)  sqrt [ 45 * 30 * 9 * 6 ]   =  

360 units^2

70 + 3x  =  80 + 2x

3x - 2x =  80  - 70

x  = 10    hours

Here's the graph :  https://www.desmos.com/calculator/lxml7xtmnl

Cost of hot dog meal  =  x

Cost of hamburger meal  = y

2x + 1y =  18     →    y  =   18 - 2x      (1)

3x  + 2y =  31     (2)

Sub (1) into (2)

3x + 2 ( 18 - 2x) =  31

3x + 36  - 4x  =  31

3x - 4x  =  31  - 36

-x =  -5

x = 5  = cost (in dollars)  of hot dog meal

Hamburger meal  costs   18 - 2(5) =   18 - 10  =  $8

See my answer under your original post

Call the nymber of friends he has, x

5x + 25  =   the total number of cupcakes  he had before baking the additional ones

Giving his friends 9 cupcakes apiece  would result in this equation

5x +  25 + 35   =  9x

5x + 60 =    9x

60   = 9x - 5x

60  = 4x

60 / 4  = x =    15  friends

The number he has baked =  5 *x + 25 =   5(15) + 25  =  100

Proof

If he bakes 35 more he has 135

And each friend would receive     135 / 15  =   9

To have two real roots, the discriminant must be >  0

So

m^2  -  4(2)(18)  >  0

m^2  >  144

This  will be true  when   m  =  ( -inf - 12)U ( 12, inf)

O + J  =  66    

O -  J =   24         add these

2O  =     90

O  = 90 / 2   =  $45  = what Oliver had  at all times

J =  $21  = what Juan had at first   

Juan had  (1/3)O  =   (1/3) (45)   =  $ 15  after the store 

He spent  21 - 15  =       $ 6 at the store

Since BY = BC

Let  angles BCY and BYC = x = angle BCA 

Then angle YBC =  180  - 2x

And angle XBY =   150 - (180 - 2x) =  2x - 30 = Angle BXY

And since AX = XY

The angles  XAY and XYA are equal

And by the exterior angle theorem, angle BXY =  2* angle  XAY= angle BAC 

2 * angle BAC = angle BXY

2 * angle BAC =   2x - 30

angle BAC = (2x - 30) / 2 =  x - 15

So

angle BAC +  angle ABC  + angle  BCA = 180

(x - 15)   +  ( 150 )  +  (x)  =  180

2x +  135  = 180

2x =  180 - 135

2x  = 45

x = 22.5

Angle BAC =  22.5 - 15 =    7.5°

Ronnie had R stamps at first

Harry  had  6R

After  Harry gave  1/2 of his stamps to Ronnie

(1/2) * 6R  + 11  =  R + (1/2) (6R)

3R + 11  =  R + 3R

3R + 11 =  4R

11 =  4R - 3R

11 = R

Harry had 6*11 =    66 stamps at first

Note that a, b   are both positive

Using some log properties

log ( a - 2b)^2  =  log (a * b)

This means that

(a - 2b)^2  =  ab

a^2 - 5ab + 4b^2  = 0

(a - 4b) ( a - b)  = 0

Either                                          

a - b=   0        

a =  b

a / b  =  1      { this may produce a log of a  negative  - not  allowed }

Or

a - 4b  = 0

a = 4b

a / b =  4

The second is  correct